MALL proof nets identify proofs modulo rule commutation
Di Guardia, Rémi, Laurent, Olivier · arXiv (Cornell University) · 2016
We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus for ⋆-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo [Vincent Balat and Roberto Di Cosmo, 1999]. This yields a much richer equational theory involving distributivity and annihilation laws. The unit-free case is obtained by relying on the proof-net syntax introduced by Hughes and Van Glabbeek [Dominic Hughes and Rob van Glabbeek, 2005]. We then use the sequent calculus to extend our results to full MALL (including all units).